British oil giant BP could begin plugging its broken oil well in the Gulf of Mexico Monday night, more than three months after its rupture led to the worst offshore oil spill in U.S. history.

BP engineers are preparing to pump heavy drilling mud and cement into the well in a procedure known as “static kill,” Coast Guard Adm. Thad Allen, the U.S. official overseeing the federal spill response, said Sunday.

Allen said that the static kill operation could start “as early as Monday night” or possibly early Tuesday. Allen told reporters he would travel to BP’s Houston headquarters to oversee the “static kill.” Engineers should know within hours whether the procedure has worked, he said.

Five to seven days later, mud and cement will be pumped in from below via a relief well that has been dug deep into the earth to seal the leak once and for all.